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Thinkport | Mapping Sculptures

In this video from MPT, learn how sculptor Mary Ann Mears uses angle measurement and geometric relationships when determining angles in scale models. In the accompanying classroom activity, students apply what they learn in the video as they solve problems in which they are given clues about two of the angles in a triangle and must determine the third. Clues involve measurements of interior and exterior angles in the triangle. To get the most from the lesson, students should be familiar with the concept of scale models. For a longer self-paced student tutorial using this media, see "Mapping Out Sculptures" on Thinkport from Maryland Public Television.

Materials: Per student: pencil, paper, Triangle Angles worksheet; for the class: a few protractors for students to use if needed; for teachers only: Triangle Angles Solutions answer key

Procedure1. Introduction and Video (10 minutes, whole group) Probe to find out what students know about sculptures, including any large geometric pieces in local public areas. Ask students for ideas on what math might be involved in planning and creating sculptures.

Play the video, pausing as follows:

At 1:06, ask students to try to determine the third angle before you continue the video to reveal the solution.

At 2:30, ask students to try to determine the measure of each angle marked with an arc mark. After a moment, ask volunteers to share their thinking. Establish that the exterior angle of each angle is 120° and that the interior and exterior angles are supplementary.

Throughout the video, also pause if needed to review any relevant terms, including congruent angles, interior angle, and equiangular triangle.

When the video is over, ask, Why is it important that Ms. Mears uses the correct angles when she makes a scale model?

2. Triangle Angles (10 minutes, individual and pairs) Distribute materials, and review instructions for the worksheet. Emphasize that students are to record how they arrived at their answers or how they know that the problem is impossible.

As students work on the sheet, circulate to see if anyone is having difficulty. You might suggest that they make a sketch to visualize and keep track of exterior and interior angle measures. If needed, call a small group together to model solving the problems and recording thinking in a step-by–step manner.

As students finish up, have them join with a partner to compare their solutions.

3. Conclusion (5 minutes, whole group) Ask for a few volunteers to share solution strategies for selected problems, including one of the “impossible” problems.

For each, keep the emphasis on how students solved the problem (e.g., How did you figure out that the problem is impossible?). As students share, model their strategies on the board using equations and/or sketches.

Wrap up with a couple of questions to help students reflect on the relationship between interior and exterior angles in a triangle:

If an interior angle is less than 90°, will the related exterior angle be more or less than 90°? How do you know?

If an interior angle is greater than 90°, could the related exterior angle also be greater than 90°? Why or why not?

Activity Extension: Pose the following for students to explore: The interior angles of a triangle sum to 180°. Do the exterior angles always sum to a certain number as well? How do you know?

You may also have students draw accurate pictures of the triangles from the Triangle Angles activity. This may help build background knowledge for when they study triangle congruency in later geometry courses.